Modelling of Fiber Metal Laminate (FML) Composite under Block Loading Using the Stiffness Degradation Model

Transcription

1 Modelling of Fiber Metal Laminate (FML) Composite under Block Loading Using the Stiffness Degradation Model S. ABDULLAH, A.FAHRUDDIN, S. JUNAIDY, M.Z. OMAR AND M.Z. NUAWI Department of Mechanical and Materials Engineering Universiti Kebangsaan Malaysia UKM Bangi, Selangor MALAYSIA Abstract: - Most of the experimental fatigue tests were performed under constant amplitude loading. However, this type of loading is hardly present in an actual condition, for which the presence of variable amplitude loading or spectrum loading is seems vital. To present the effect of variable amplitude loading with respect to the fatigue failure of composite-based materials, thus, it is an idea to perform or to simulate the case using a set of block loading with various amplitude of low-high and high-low sequences. Perhaps, these sequences can be used for simulation and experimental purposes. In this paper, the authors discussed the effect of block loading towards the damage development in Fiber Metal Laminate (FML) composites. The simulation work was performed using the available stiffness degradation model, and the results were validated using the experimental data. Keywords: FML, block loading, fatigue, degradation model, composite 1. Introduction Fiber Metal Laminates (FML) is a kind of hybrid materials and it can be fabricated from an alternating laminate of thin metal sheets and thin composite layers. Since several variables are involved in the composition of this laminate, a wide range of different combinations lamination seems to be possible. Some of these variables are the type of metal alloy, the type of fibers, the type of polymer, the thickness of layers, the number of layers, the orientation of (fibrous) layers, etc. Therefore, FMLs are regarded as a family of laminates, and GLARE is the best-known member of these laminates. GLARE is made from aluminum layers in the range of mm thick, and glass fiber reinforced composite layers in the range of mm thick [1]. One of the wide used of GLARE composite is in aeronautic application. Based on the expected growth of passengers for intercontinental flights within the world, high capacity aircraft (such as from the Airbus company) are currently developed. To make this airplane cost effective for the next 30 years, new technologies are being evaluated such as the application of new aircraft materials. One of these studies investigates the feasibility of using the FML in the upper part of the aircraft that needs to be fatigue failure resistant, or specifically the structure should be under damage tolerant design [2]. GLARE composites have better resistance characteristics, such as high fatigue resistance, and also having an improved resistant in corrosion, particularly in the extreme temperature [3]. As early as 1923, Palmgren [4] published hypothesis which is now generally known as the Miner rule or the linear cumulative damage hypothesis. According to Palmgren applying n times a cycle with a stress amplitude S and a corresponding fatigue life N is equivalent to consuming a portion of n/n of the fatigue life. Failure occurs when 100% of fatigue life is consumed. A failure thus occurs when: n = 1 (1) N However, Palmgren did not give any physical derivation for the rule. He was in need for an estimate of the fatigue life under Variable Amplitude (VA)-loading, and he adopted the simplest assumption for fatigue damage accumulation. Miner introduced the idea that the fatigue damage that fatigue damage is the consequence of work absorbed by the material which was assumed to be proportional to the number of cycles [5]. The new model was formulated by Van Paepegam and Degrieck [6], for which this model is capable to simulate three stages of stiffness degradation that can be found in FML materials, ISSN: ISBN:

2 i.e. sharp initial decline; gradual deterioration; final failure. Since this model was already applied in fiber reinforced composites, thus, it is assumed that it can be also implemented for the FML composites. The objective of this paper is to numerically simulate the fatigue lives under block loading in the FML GLARE based on experimental data. In order to achieve the objective, it is vital for the authors to observe the failure high-low sequence or the low-high sequence cycles gave more failure in FML GLARE material under block loading. 2. Literature Background 2.1 Composites Fiber Metal Laminate can be said to have a high fatigue resistance, with it is achieved by the intact bridging fibers in the wake of the crack. This condition restrains the occurrence of the crack opening [7]. Controlled delaminating in the material makes some crack opening possible without failure of the fibers. The fibers transfer load over the fatigue crack in the metal layer and restrain the crack opening. This phenomenon is called fiber bridging [8]. The fatigue fibers laminates can be formed and machined like aluminum alloys and have the high specific strength of composite materials: they combine the best of both worlds. The laminates can be applied in various thicknesses, e.g. a 2/1 lay-up means a laminate with two aluminum layers and one intermediate fiber/epoxy layer: [A1/prepeg/A1]. The fiber/epoxy layer at 2/1 lay-up can be multiple cross plied 0/90 layer or be unidirectional [9]. 2.2 Fatigue Damage Formulation The used of the phenomenological model for this study is based on the residual stiffness approach. Hence, the stress and strain are related by the commonly used equation in continuum damage mechanics. This stiffness degradation model, which is applicable for fatigue life assessment for a FML composite, was developed by Van Paepegam and Degrieck [6]. It can be said as an improved model to date for the analysis of a FML specimen under a cyclic pattern of constant and variable stress/strain loadings. This model is mathematically defined as the following equation: σ = E ε 1 D = (2) σ 0 Where σ is the effective stress, σ is the applied nominal stress, ε is nominal strain, E 0 is the undamaged Young s modulus. From Equation (2), the fatigue damage value can be calculated using Equation (3): D = 1 E / E (3) 0 The damage (D) value is lying between zero (virgin material state) and one (final failure). The main drawback of the residual stiffness models is that they do not provide a means to estimate the moment of final failure. This problem is solved by establishing a relation between the damage variable D (measure for the residual stiffness) and a fatigue failure index. The fatigue failure index is the ratio of applied effective stress σ to the static strength; it has value between zero and (applied stress equal zero) and one (effective stress equal static strength). This measure for the applied stress in relation to the static strength is now used in the damage growth rate equation dd / dn that is given by: dd D 2 = c1. Σ.exp( c2. ) + c3. D. Σ.[1 + exp( c5( Σ c4))] dn Σ (4) In the damage growth rate of the damage equations, all five constants c i (i=1,,5) have a distinctive meaning [11]: c 1 Regulates the growth rate of the damage initiation regime (and thus the sharp initial decline of the modulus degradation curve), c 2 Is sufficiently large, so that the first term disappears when damage increases. Then, the steady state of matrix cracking, the so-called characteristic Damage State has been reached c 3 Represent the growth rate in the second stage of modulus degradation. Additional damage mechanism (fiber/matrix delaminating, pull-out from fibers out the matrix, initial fiber breakage) are developing gradually in the stage of fatigue life, ISSN: ISBN:

3 c and c 5 express the explosive damage growth once that the failure index Σ ( σ, D) approach its failure 1.0 and the 4 effective stress σ approaches the static strength in tension or compression. When the threshold c 4 has been crossed, fiber fracture starts to propagate and finally causes failure in that material point. 12 cm 3 cm Fiber/epoxy 3. Methodology Aluminium 3.1 Experimental Works In order to prepare the FML specimen, the open mold process was used, and this mold was fabricated using a steel type material. During the lamination process, the combination fabricating and curing procedure of aluminum plate and resin were accounted for. The gel coating procedure was then applied in order to obtain a good surface finish of the specimen. The fabrication process of FML specimen used hand lay-up method, for which the fiber and epoxy were manually placed, and the excessive air was drawn using a vacuum bag. The hardening procedure was carried out within the room temperature. This process was accelerated with an additional heating and also mixed with an additional hardener. The FML curing process was performed up to 120 C with the heating rate of 2.5 C/min. In order to avoid the trapped air in the prepreg, the vacuum bag was then used. This prepreg was covered by a vacuum bag and it was positioned in the autoclave for the curing procedure. The sample of specimen produced using the stated methodology is shown in Fig. 1. The other method that can be used for the specimen preparation is hot compress with the similar pressure and temperature [10]. Due to the lack facility of this hot compress method, this alternative procedure cannot be performed. Fig.1. The geometry and shape of FML specimen used in this study The strength test has been carried out for several FML specimens. The tests were performed using the 25 ton capability of a servohydraulic power universal testing machine. Using the tensile test, the properties of the tensile strength and also tensile modulus of the specimens can be obtained, as tabulated in Table 1. Fig. 2 shows a FML specimen fitted at the universal tensile testing machine before the test. Fig. 2 A FML specimen fitted at the universal tensile machine 3.2 Damage Growth Observation The model of Equation (1) was computationally simulated using the material properties listed in table 1. These values were obtained from the tensile test specimens. These values then will be used with literature based model parameters in order to obtain the damage growth estimation of a specimen. ISSN: ISBN:

4 Table 1. Material properties obtained in the experiment and the literature-based model parameters Material properties Model Parameters XT c Yield Strength c (MPa) Yield Strength, offset 2% (MPa) Elasticity Modulus (GPa) c 3 4 x c c From the simulation works using the parameters in Table 1 and the mathematical model of Equation (4), it shows that the damage growth of material significantly increases when the FML specimen was slightly failed or the value of damage equal to 1, and this damage growth trend is plotted in Fig. 3. It shows that the damage growth is significantly increased when the damage value between 0.9 to 1. σ ( Χ 919MPa) Χ i Τ = Τ Fatigue life [Number of cycles to failure] (a) (b) Fig. 4 The schematic diagram of the loads applied in the study: (a) low-high sequences, (b) high-low sequences. Fig. 3 Damage Growth of a FML specimen based on the model in Equation (4) 3.3 Load Sequence Effects Fig. 4 shows schematic the diagram of the load sequences applied in the simulation. These two sequences were computationally used in order to observe the fatigue damaging effect under block loading, which is due to the transition from low to high stress levels. The fatigue lives for certain constant amplitude stress levels (0.4, 0.5, 0.7, and 0.8) is tabulated in Table 2. In the simulation analysis, the high-low and low-high load sequences were modeled using the related formulation of Equation (2)-(4). The second block sequence (in the respective block loading) were then applied after the damage value of the first block was calculated and gave the value of 0.5 according to the Palmgren-Miner s linear summation method. For the high-low load sequence, therefore, it was shown that as many as cycles has been estimated at the stress level of 0.6X T, and followed by a run out at the stress level of 0.4X T. The damage evolution for both load sequences is shown in Fig 5. Fig 6 shows the same cycles of the high-low load sequences have larger damage potential compared to the low-high load sequences. In this figure the number of cycles to failure index is shown for both load sequences. In this case, the high-low load sequences gave more effects to the delamination occurrence of FML under cyclic loadings. Table 2. Number of cycles and block loadings used for the load sequence effects analysis ISSN: ISBN:

5 The transition from a high stress level to a low stress level was more damaging cycle sequence effect. It is because of the damage than from high to low it was caused high cycle amplitude. In addition, the effective stress was also increased more than the applied nominal stress. parameter. These values were obtained from the tensile test and also from literature. Using both experiment and simulation data, it can suggested that the load sequences transition from a high stress level to a low stress level was more damaging cycle sequence compared to a low stress level to a high low stress level was more damaging cycle sequence. In this case, a FML-specimen is said to be at failure condition when there is delamination effects between laminates and also the occurrence of small crack on the specimen surface. Finally, it is also concluded that the damage growth of material was significantly increased when the material damage value in between 0.9 to 1, according to the Palmgren-Miner s linear damage rule. Fig 5. Comparison of the damage curve between the high-low and the low-high load sequences Fig. 6 A plot of cycles history of the FML-based materials fatigue damage against the fatigue failure index 4. Conclusions The fatigue damage model had been used to simulate the effect of block loading on fatigue test with FML composites. The simulation of FML damaging under block loading was due to transition from low to high stress levels and from a high stress level to a low stress level. The model was computationally modelled using the material properties and literature-based References: [1] Vlot, A, Vogelesang, L.B., Towards application of fiber metal lamination in large aircraft, Aircraft Engineering and Aerospace Technology: An International Journal, Vol. 8(7), 1999, pp [2] Sinke, J, Manufacturing of GLARE parts and structures, Applied Composite Materials, Vol. 10, 2003, pp [3] Alderliesten, R.C., Fatigue Crack Propagation and Delamination Growth in Glare, Delft University Press, 2005 [4] Theodore, P., Vassilopoulos, A., Life prediction methodology for GFRP laminates under spectrum loading, Applied Science and Manufacturing Journal, Vol. 25, 2004, pp [5] Schijve, J., Fatigue of structure and materials in the 20 th century and the state of the art, Material Science Journal, No. 25, 2003, pp [6] Van Paepegem, W., Degrieck, J., Effects of load sequence and block loading on the fatigue response of fiber reinforced composites, Mechanics of Advance Material and Structure, Vol. 9(1), 2002, pp [7] Vlot, A., Gunnink, J.W., Fibremetal Laminates: An Introduction, Kluwer Academic Publishers, [8] Alderliesten, R.C., Analytical prediction model for fatigue crack propagation and delamination growth in Glare, International Journal of Datigue, No. 19, 2007, pp [9] Shim, D.J., Alderliesten, R.C., Fatigue crack growth prediction in Glare hybrid ISSN: ISBN:

6 laminates, Composite Science and Technology, No. 13, 2003, pp [10] Botelho, E.C., Pandini, L.C., Hygrothermal effect on damping behavior of metal/glass fiber/epoxy hybrid composite, Material Science and Engineering, No. 39, 2005, pp [11] Van Paepegem, L.C., Degrieck, J., A new coupled approach of residual stiffness and strength for fatigue of fiber reinforced composite, International Journal of Fatigue, No. 24, 2002, pp ISSN: ISBN: